Existing models[1]} of price processes as smooth continuous processes begin to disconnect with reality at the micro perspective. Exchanges that actively use limit order books process orders at discrete price levels, and thus there is no real "price", but instead of history of past transactions and outstanding, unfilled orders. Transactions take place at discrete price levels, so the time series evolution of the transactions exhibits jumps, the effect of which become more profound at smaller time scales. In the past some academics have advocated for the use of continuous time models for market micro-structure, and subsequently introduced a framework based on point processes [2]}, [3]}. Since this time, the study of point processes, and in-particular Hawkes processes, have been the focus of an increasing amount of academic study[4]}, [5]}.
